Mechanism of Chiral Symmetry Breaking

According to the generally accepted theory of strong interactions, Quantum Chromodynamics (QCD), the vacuum is non-trivial. It is filled with quantum fluctuations and topological excitations. The colour field between quarks and antiquarks, on the other hand, has a regular Coulombic structure and expels quantum fluctuations and topological excitations from the region of strong fields. This leads to narrowing of the flux lines, a small gluonic flux tube, the gluon string, and therefore a linear potential between quarks and antiquarks, and the confinement of quarks. For large distances the width and therefore the strength of the flux tube is determined by the density of topological excitations. The vortex model assumes that the important topological excitations are closed colour magnetic flux lines, the vortices. During the last years our group was able to show numerically that the vortex model is able to explain the strength of the gluonic flux tube, the string tension. For massless quarks the Lagrangian of QCD does not lead to an interaction of right- and left-handed quarks, of quarks with spins directed in and against the direction of momentum. This is the chiral symmetry of the QCD Lagrangian. The numerical investigations show that confinement is always connected with a dynamical coupling of right and left-handed quarks, a dynamical breaking of chiral symmetry. This suggests that the topological excitations which are responsible for confinement are also the origin of the dynamical symmetry breaking. In first calculations to the chiral symmetry breaking of vortex configurations it was possible to show a relation between vortices and chiral symmetry breaking. But the mechanism for this relation is not yet understood. It is the purpose of the project, to find this mechanism. Next to confinement, chiral symmetry breaking is the most important low-energy phenomenon in QCD, and a full understanding of this effect is of vital importance. A successful and unified picture of both confinement and chiral symmetry breaking would be an important advance, and ought to be of great interest to broad sections of both the lattice and nuclear physics communities.

According to the generally accepted theory of strong interactions, Quantum Chromodynamics (QCD), the vacuum is non-trivial. It is filled with quantum fluctuations and topological excitations. The colour field between quarks and antiquarks, on the other hand, has a regular Coulombic structure and expels quantum fluctuations and topological excitations from the region of strong fields. This leads to narrowing of the flux lines, a small gluonic flux tube, the gluon string, and therefore a linear potential between quarks and antiquarks, and the confinement of quarks. For large distances the width and therefore the strength of the flux tube is determined by the density of topological excitations. The vortex model assumes that the important topological excitations are closed colour magnetic flux lines, the vortices. During the last years our group was able to show numerically that the vortex model is able to explain the strength of the gluonic flux tube, the string tension. For massless quarks the Lagrangian of QCD does not lead to an interaction of right- and left-handed quarks, of quarks with spins directed in and against the direction of momentum. This is the chiral symmetry of the QCD Lagrangian. The numerical investigations show that confinement is always connected with a dynamical coupling of right and left-handed quarks, a dynamical breaking of chiral symmetry. This suggests that the topological excitations which are responsible for confinement are also the origin of the dynamical symmetry breaking. In first calculations to the chiral symmetry breaking of vortex configurations it was possible to show a relation between vortices and chiral symmetry breaking. But the mechanism for this relation is not yet understood. It is the purpose of the project, to find this mechanism. Next to confinement, chiral symmetry breaking is the most important low-energy phenomenon in QCD, and a full understanding of this effect is of vital importance. A successful and unified picture of both confinement and chiral symmetry breaking would be an important advance, and ought to be of great interest to broad sections of both the lattice and nuclear physics communities.